On the number of Courant-sharp Dirichlet eigenvalues
classification
🧮 math.SP
math.AP
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courant-sharpdirichletomegaeigenvaluesnumberarbitraryboundsconsider
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We consider arbitrary open sets $\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of $\Omega$. This extends recent results of P. B\'erard and B. Helffer.
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